--- title: 02d Flow Datasets keywords: fastai sidebar: home_sidebar summary: "Here be the tailored datasets for FRED! In addition to storing points, we must store a graph, and intelligently sample from the graph so that batches preserve 'flow neighborhoods'" description: "Here be the tailored datasets for FRED! In addition to storing points, we must store a graph, and intelligently sample from the graph so that batches preserve 'flow neighborhoods'" nb_path: "02d Flow Datasets.ipynb" ---
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As previously listed, this is our preprocessing pipeline.

  1. Turn data to torch tensors
  2. Build graph from data, using flashlight kernel
    1. Estimate best parameters for kernel selection
  3. Take diffusion map on data (or any ‘best guess embedding’) we want to penalize against. (Can be done on CPU or GPU). Would likely use established methods, like PHATE, tSNE, node2vec.
    1. Visualize embedding
  4. Find flow neighborhoods of data (possibly at multiple scales)
  5. Break data into batches (both affinity matrix of batches and points in batches).
  6. Return Dataloader with minibatch X and subgraph A of each batch.

0-3 are handled by separate functions. This notebook calls upon these functions, and implements the machinery for 4 and 5

Two Types of Data

FRED can operate on both directed graphs (assumed to be sampled from a manifold with flow, ala the "Manifold with Flow" hypothesis) and pointclouds with associated velocity vectors (like RNA velocity single cell data). Each type is processed differently, and requires a different dataset class.

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class ManifoldWithVectorField[source]

ManifoldWithVectorField(X, velocities, labels, sigma='automatic', prior_embedding='diffusion map', t_dmap=1, dmap_coords_to_use=2, n_neighbors=5, minibatch_size=100, nbhd_strategy='flow neighbors') :: Dataset

Dataset object to be used with FRED for pointcloud and velocity input data. Takes np.arrays for X (points) and velocities (velocity vectors per point). For each item retrieved, returns a neighborhood around that point (based on local euclidean neighbors) containing local affinities

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Testing

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from FRED.datasets import directed_swiss_roll_delayed
X, flow, labels = directed_swiss_roll_delayed(num_nodes=1000)
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ds = ManifoldWithVectorField(X, flow, labels)

Set sigma =  2.3770864
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for data in ds:
    print(data)

{'P': tensor([[4.0173e-02, 2.0302e-01, 1.4001e-01,  ..., 3.0227e-06, 7.4944e-05,
         9.0509e-05],
        [5.7301e-03, 4.8314e-02, 1.7639e-01,  ..., 3.6155e-06, 1.1521e-04,
         1.3691e-04],
        [3.7528e-03, 5.3394e-03, 5.2184e-02,  ..., 5.4380e-06, 2.1628e-04,
         2.7195e-04],
        ...,
        [4.0596e-05, 3.4174e-05, 3.4960e-05,  ..., 5.3405e-01, 4.7545e-05,
         5.5604e-05],
        [9.8737e-07, 9.0580e-07, 8.7754e-07,  ..., 1.1897e-05, 4.3833e-03,
         1.0262e-05],
        [6.1747e-06, 5.9572e-06, 6.7358e-06,  ..., 3.8245e-04, 1.7551e-01,
         3.5869e-02]]), 'X': tensor([[  0.1206,  -4.7363,   8.7103],
        [  0.6952,  -4.8060,   8.8976],
        [  1.7228,  -4.7575,   8.3396],
        [  0.9074,  -4.8139,   8.1674],
        [  2.1120,  -4.6818,   8.6144],
        [  2.1504,  -4.6726,   8.7908],
        [ -8.0750,  -6.0072,  -5.8267],
        [ -6.4002,  -8.1048,  -0.9108],
        [ -0.0410,   7.8591,   9.3457],
        [ -9.4748,  -0.7765,  -5.6695],
        [ -8.0330,  -6.0765,   6.7945],
        [  6.3516,   0.6425,   0.3425],
        [  3.2701,   6.6338,   9.9209],
        [  6.1685,  12.1979,  -6.2473],
        [  8.3791,  10.5409,   5.5590],
        [  4.5954,  13.0099,  -4.4439],
        [ 10.4994,  -5.9193,  -7.5153],
        [ -8.5900,   2.9767,   7.4811],
        [  5.6672,  -1.8631,   8.1020],
        [ 12.1588,   4.3364,  -8.0867],
        [  2.0547,   7.2957,  -1.9343],
        [ -4.0868,   7.2981,   8.1874],
        [ 10.2712,   8.3707,  -4.9743],
        [ -7.9298,   4.1367,  -3.9773],
        [ -9.0961,   1.6529,   3.1553],
        [  6.1989,  -9.7591,   0.8289],
        [  9.2811,  -7.4336,   5.1771],
        [  2.5318,  13.7231,   6.3692],
        [  8.5093,  -8.1764,  -3.2381],
        [  6.2535,  -0.1709,  -9.4102],
        [  5.0190,   4.9705,  -7.9752],
        [  1.5383, -11.0274,  -4.9666],
        [ -3.2486,   7.5925,  -1.3719],
        [ 10.8670,  -5.3428,  -2.8637],
        [  6.1575,  12.2046,   3.3257],
        [  2.2373,  -4.6506,  -1.7334],
        [ 11.9936,  -2.8677,   6.0614],
        [  6.3460,   1.4252,   1.2291],
        [ 12.5717,   1.9266,   7.4903],
        [ -6.3306,   5.9272,   5.6935],
        [  4.3523, -10.5232,   8.2138],
        [ -9.4501,  -1.7133,   2.2980],
        [ -7.0120,   5.2825,   7.7762],
        [  6.8093,  -9.4178,   8.4244],
        [ -9.4671,  -0.5553,   0.1117],
        [  6.0073,   3.0986,   6.7937],
        [ -7.3446,   4.9113,  -5.9356],
        [ 12.2311,  -2.0445,   1.3545],
        [ -6.1914,  -8.2997,   8.5380],
        [  4.0457,  -3.7737,  -0.4704],
        [ -8.0750,  -6.0072,  -5.8267],
        [ -9.4505,  -1.7081,  -0.7039],
        [ -9.1960,  -3.2964,   1.6921],
        [  4.5800,   5.5034,  -3.9432],
        [  6.3587,   1.1596,  -3.6629],
        [  6.2905,   1.9366,   2.1169],
        [ 11.1085,  -4.9204,   0.0736],
        [  5.9526,   3.2525,  -4.3821],
        [  5.1861,   4.7361,  -3.7312],
        [ -5.0943,  -9.1682,   0.5073],
        [  2.7590,  13.6621,   9.4496],
        [ 11.9641,  -2.9568,   7.7211],
        [  5.1890,   4.7318,   0.9515],
        [ -5.7347,  -8.6908,   9.2878],
        [ -7.4807,   4.7463,   2.0616],
        [  2.1379,  -4.6757,   6.4981],
        [  6.0345,   3.0175,  -1.4424],
        [  6.0140,  -1.0661,  -2.5040],
        [  2.4572,   7.1085,   7.7376],
        [ -7.5720,   4.6310,   2.1717],
        [  5.6093,  -1.9705,   6.4807],
        [ 11.7162,   5.6728,  -8.9372],
        [ -6.4822,  -8.0252,  -3.8983],
        [  2.0039,   7.3173,  -1.5885],
        [ -1.6334, -10.7207,   7.1397],
        [  6.3497,   1.3680,  -1.9076],
        [  6.3606,   0.9204,   3.2525],
        [ 12.6000,   1.3839,  -3.2992],
        [ 11.5935,   5.9740,  -4.3952],
        [ 11.7418,   5.6070,  -1.4192],
        [  6.1372,   2.6726,  -6.7885],
        [  0.6933,   7.7336,   2.1179],
        [  6.3200,   0.2690,   1.5900],
        [ 11.7418,   5.6070,  -1.4192],
        [  3.3839,  -4.1966,   8.3574],
        [ -1.5408,   7.8978,   5.3470],
        [  9.5203,   9.3483,   5.8781],
        [  5.8979,   3.3958,  -3.8713],
        [  6.0073,   3.0986,   6.7937],
        [ -9.3384,  -2.6161,  -4.7630],
        [  0.9659,  -4.8144,  -0.9594],
        [  5.3860,  -2.3418,   1.0826],
        [  4.1348,   5.9514,  -0.8856],
        [  6.1222,  -0.7261,   8.8204],
        [ -9.0961,   1.6529,   3.1553],
        [  1.5653,  13.9377,   4.1773],
        [  5.7151,  -1.7700,   3.1542],
        [ -1.6275, -10.7221,   3.2376],
        [  1.8719,   7.3713,  -3.7465],
        [ 11.9936,  -2.8677,   6.0614],
        [  5.5294,  -2.1106,   9.0626],
        [ -9.4524,  -1.6813,  -6.6862],
        [ -6.9838,  -7.4965,   0.9796],
        [ -0.2586,   7.8825,  -9.9840],
        [  9.0051,   9.9234,   5.4411],
        [ 11.1469,   6.9237,   1.6160]]), 'num flow neighbors': 5, 'precomputed_distances': tensor([[0.0000, 0.0183, 0.0397,  ..., 1.0319, 0.4221, 0.4737],
        [0.0183, 0.0000, 0.0250,  ..., 1.0408, 0.4039, 0.4658],
        [0.0397, 0.0250, 0.0000,  ..., 1.0334, 0.3858, 0.4422],
        ...,
        [1.0319, 1.0408, 1.0334,  ..., 0.0000, 1.2644, 0.8532],
        [0.4221, 0.4039, 0.3858,  ..., 1.2644, 0.0000, 0.4443],
        [0.4737, 0.4658, 0.4422,  ..., 0.8532, 0.4443, 0.0000]]), 'neighbors': tensor([[0., 0., 0., 0., 0.],
        [1., 2., 3., 4., 5.]]), 'labels': array([ 4.73784222,  4.85603886,  5.05981914,  4.89869205,  5.13616224,
        5.14371005, 10.06437598, 10.32715715,  7.85919687,  9.50654967,
       10.07238463,  6.38399789,  7.39599986, 13.66896739, 13.46553623,
       13.79762415, 12.05300943,  9.09119351,  5.96556248, 12.9089559 ,
        7.57946459,  8.36445758, 13.25017211,  8.94395628,  9.24501829,
       11.56146873, 11.89105259, 13.95472331, 11.80092578,  6.25586297,
        7.06372172, 11.1341798 ,  8.25828409, 12.10942412, 13.66991027,
        5.16077764, 12.33167382,  6.50409372, 12.71843462,  8.67227386,
       11.38774149,  9.60412735,  8.77913428, 11.62158554,  9.48337063,
        6.7593917 ,  8.8353674 , 12.40074901, 10.35464916,  5.53255882,
       10.06437598,  9.60359158,  9.76896904,  7.15990676,  6.46356806,
        6.58184474, 12.1494023 ,  6.78325151,  7.02326515, 10.48840476,
       13.93790235, 12.32408516,  7.02253235, 10.412299  ,  8.85939626,
        5.14124612,  6.74686071,  6.10774544,  7.52117132,  8.87587457,
        5.94535529, 13.01728313, 10.31613269,  7.58668144, 10.84437705,
        6.49538841,  6.42689705, 12.67576792, 13.04217487, 13.01187484,
        6.69389431,  7.76457095,  6.32572323, 13.01187484,  5.39098669,
        8.04664886, 13.3426541 ,  6.80559669,  6.7593917 ,  9.69792513,
        4.91038884,  5.87305005,  7.24677664,  6.16512856,  9.24501829,
       14.02532758,  5.98285319, 10.84493732,  7.60529892, 12.33167382,
        5.91854397,  9.60080639, 10.24557047,  7.88677538, 13.40024224,
       13.12218013])}
{'P': tensor([[4.9490e-02, 1.5156e-01, 1.3517e-01,  ..., 2.1036e-03, 6.0857e-05,
         3.0897e-05],
        [3.4654e-03, 5.6177e-02, 2.6353e-02,  ..., 6.2701e-04, 4.8607e-05,
         2.8119e-05],
        [4.9679e-03, 5.4702e-02, 7.0618e-02,  ..., 1.0231e-03, 7.1857e-05,
         4.5569e-05],
        ...,
        [6.7935e-04, 1.7123e-03, 2.2919e-03,  ..., 1.5085e-02, 1.3171e-06,
         1.0505e-06],
        [5.6071e-04, 2.1301e-04, 2.8238e-04,  ..., 3.6791e-04, 2.9155e-02,
         5.6511e-04],
        [1.2404e-04, 5.3041e-05, 7.6161e-05,  ..., 8.7878e-05, 2.9782e-02,
         2.8419e-02]]), 'X': tensor([[  0.1532,  -4.7422,  -7.0145],
        [  2.0899,  -4.6870,  -7.4260],
        [  1.9503,  -4.7172,  -6.2313],
        [  0.8700,  -4.8132,  -7.8042],
        [  3.1480,  -4.3165,  -7.8002],
        [  3.2990,  -4.2415,  -7.4857],
        [ -6.8618,  -7.6322,   3.7027],
        [ -7.5401,   4.6718,   9.0033],
        [  5.9003,  12.3550,   2.1917],
        [ -0.8675, -10.8815,   6.8561],
        [  5.8979,   3.3958,  -3.8713],
        [ -9.1795,  -3.3623,   8.5259],
        [  3.8182,  -3.9347,  -1.7961],
        [ -5.2752,  -9.0409,  -8.2568],
        [  9.5261,  -7.1675,   1.4206],
        [  0.9445,   7.6736,   0.5095],
        [ -0.0410,   7.8591,   9.3457],
        [  5.4732,  -2.2041,  -4.3830],
        [ -8.8154,   2.4611,   2.5198],
        [ -8.3900,   3.3727,   3.1650],
        [ -9.4624,  -0.4633,  -7.3918],
        [ 12.6035,   0.7494,   7.1536],
        [  6.2365,  -0.2578,  -6.0212],
        [ -8.6801,   2.7809,  -0.8443],
        [  0.5600, -11.0321,  -0.8660],
        [  4.7544,  -3.1425,  -1.5315],
        [  0.9967,  -4.8144,  -9.7370],
        [  5.6523,   3.9443,  -2.9449],
        [  0.9074,  -4.8139,   8.1674],
        [ 12.2435,   4.0076,   8.1257],
        [  6.0305,   3.0296,   0.1375],
        [  0.6142,  14.0802,   0.5407],
        [  6.2419,  -0.2313,   4.2440],
        [  0.3715,  -4.7756,   0.2312],
        [ 12.4901,  -0.7052,   1.7315],
        [ -2.6735, -10.4062,  -1.5911],
        [  4.0642,  -3.7599,  -3.4565],
        [ -3.9508,  -9.8515,   1.7923],
        [ -7.5603,   4.6459,   8.2002],
        [  6.9693,  -9.3200,  -8.3822],
        [  3.9663,   6.1018,  -5.4104],
        [ -7.3470,  -7.0615,   5.0066],
        [  6.3606,   0.9204,   3.2525],
        [  6.1730,  -0.5375,  -8.8861],
        [ -7.4808,   4.7462,   2.0266],
        [ -4.2040,   7.2486,   2.9875],
        [  3.1892, -10.8220,  -6.8409],
        [ -9.0574,   1.7801,   8.8986],
        [ -6.3306,   5.9272,   5.6935],
        [ -9.3705,   0.4208,  -3.5815],
        [ 11.8951,  -3.1570,   7.0742],
        [ -8.9606,  -4.0994,   1.7886],
        [  5.8318,   3.5567,  -4.7692],
        [  8.3791,  10.5409,   5.5590],
        [  7.9141,  -8.6656,   9.6948],
        [ -5.6792,  -8.7352,   4.0318],
        [ 11.2767,  -4.6006,   0.7868],
        [  4.9337,  12.8566,  -3.6582],
        [  6.5428,  -9.5728,  -2.9897],
        [  6.2036,   2.4030,  -1.2500],
        [ -0.3432,   7.8900,   7.1805],
        [  6.0467,  -9.8369,  -6.5816],
        [  6.0955,   2.8210,  -4.3321],
        [ -9.4735,  -0.7274,  -2.6749],
        [ -8.5607,  -5.0938,  -5.4531],
        [  9.0424,  -7.6779,  -7.5286],
        [  6.1685,  12.1979,  -6.2473],
        [  2.7558,  -4.4844,   0.0636],
        [  0.3724,   7.7974,  -6.8722],
        [  2.7685, -10.8982,  -6.8928],
        [  9.3560,   9.5391,   9.4943],
        [  5.0506,   4.9277,  -9.5094],
        [ -2.5056,   7.7720,   5.5878],
        [ -7.8280,   4.2848,  -7.1955],
        [ -6.8466,  -7.6488,   1.9648],
        [  4.5325,  -3.3643,   6.7699],
        [  6.3413,   0.4883,  -6.8416],
        [ -5.1369,   6.7755,   8.3836],
        [ 11.3800,  -4.3919,   1.4066],
        [ 11.7418,   5.6070,  -1.4192],
        [ -0.8885,   7.9160,   0.0571],
        [ 11.5198,  -4.0923,   5.5088],
        [  6.2576,   2.1359,  -3.3398],
        [ 11.5083,  -4.1177,   0.2389],
        [ 11.9695,  -2.9407,  -6.3498],
        [  2.1771, -10.9776,  -3.2007],
        [  1.7218,  -4.7576,  -3.3617],
        [  1.7659,   7.4127,   4.7871],
        [  2.3889,  -4.6082,  -8.7291],
        [  3.3167,   6.6022,   6.3554],
        [ 12.2328,  -2.0376,  -1.1234],
        [ -9.2373,  -3.1225,  -8.9763],
        [ -9.3107,  -2.7697,  -3.2919],
        [  0.2480, -11.0153,  -3.0183],
        [  3.2226,  -4.2802,  -4.0428],
        [  2.3490,  -4.6199,  -4.2489],
        [ -9.4159,  -2.0739,   9.6841],
        [  5.9883,   3.1536,   6.2320],
        [ -8.0534,  -6.0429,   2.4583],
        [ -9.4766,  -1.1116,  -2.1706],
        [ -8.6801,   2.7809,  -0.8443],
        [ 12.5123,  -0.5339,  -1.0728],
        [  3.1756, -10.8247,   6.8882],
        [  0.2480, -11.0153,  -3.0183],
        [ -8.8058,   2.4850,  -1.7425],
        [ -7.5720,   4.6310,   2.1717]]), 'num flow neighbors': 5, 'precomputed_distances': tensor([[0.0000, 0.0558, 0.0430,  ..., 0.5594, 0.7104, 0.7581],
        [0.0558, 0.0000, 0.0434,  ..., 0.6129, 0.7656, 0.8109],
        [0.0430, 0.0434, 0.0000,  ..., 0.5960, 0.7433, 0.7742],
        ...,
        [0.5594, 0.6129, 0.5960,  ..., 0.0000, 0.1784, 0.4564],
        [0.7104, 0.7656, 0.7433,  ..., 0.1784, 0.0000, 0.3600],
        [0.7581, 0.8109, 0.7742,  ..., 0.4564, 0.3600, 0.0000]]), 'neighbors': tensor([[0., 0., 0., 0., 0.],
        [1., 2., 3., 4., 5.]]), 'labels': array([ 4.74468406,  5.13182506,  5.10444097,  4.89121805,  5.34250225,
        5.37343173, 10.26327895,  8.87007495, 13.69162795, 10.91601655,
        6.80559669,  9.77588801,  5.48276038, 10.46739073, 11.92133129,
        7.73151309,  7.85919687,  5.90035324,  9.15253344,  9.04255655,
        9.47369628, 12.62576026,  6.24187044,  9.11473391, 11.04629471,
        5.69913817,  4.91652556,  6.89245352,  4.89869205, 12.88270018,
        6.74872981, 14.09357547,  6.24614905,  4.79003361, 12.50996828,
       10.74409834,  5.5366698 , 10.61417181,  8.8737556 , 11.63765273,
        7.27759233, 10.19036081,  6.42689705,  6.19633139,  8.859416  ,
        8.37954853, 11.28215429,  9.23071698,  8.67227386,  9.37989631,
       12.30695098,  9.85384623,  6.83083863, 13.46553623, 11.73567759,
       10.41909211, 12.17901033, 13.77075174, 11.59512194,  6.652742  ,
        7.89745107, 11.54672755,  6.7166297 ,  9.5014146 ,  9.96152788,
       11.86239961, 13.66896739,  5.26342203,  7.80625981, 11.24434374,
       13.3614598 ,  7.05627461,  8.16584537,  8.92395381, 10.26545792,
        5.64464807,  6.36004393,  8.50268322, 12.19805394, 13.01187484,
        7.96575782, 12.22503754,  6.61211224, 12.22276278, 12.32545637,
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        [  4.9957,  -2.8705,   6.5978],
        [  8.0877,  -8.5297,  -1.1050],
        [  0.2435,   7.8191,  -6.4709],
        [  3.9022,  13.2906,   5.5788],
        [  0.1497,   7.8334,  -5.4412],
        [ 11.7795,  -3.4697,   3.5624],
        [  0.6933,   7.7336,   2.1179],
        [ -8.9942,  -3.9990,   6.0448],
        [ -6.2668,   5.9808,   2.5614],
        [ -7.6293,  -6.6859,  -5.5161],
        [  1.7218,  -4.7576,  -3.3617],
        [ 11.5456,   6.0861,   8.1101],
        [  5.2199,   4.6861,  -1.9304],
        [  0.9659,  -4.8144,  -0.9594],
        [  1.1994,   7.6035,   2.4295],
        [  4.7544,  -3.1425,  -1.5315],
        [  3.3069,   6.6089,   8.7377],
        [  7.9816,  10.8938,  -0.5378],
        [  4.1297,  -3.7098,  -3.9838],
        [ -4.4520,   7.1370,  -8.7867],
        [ 12.0772,  -2.6014,  -7.1832],
        [  3.9515,  -3.8425,   6.1729],
        [ 10.8218,  -5.4177,   6.8573],
        [  6.3200,   0.2690,   1.5900],
        [  4.8051, -10.3703,   0.5268],
        [  4.5767,   5.5071,   3.9069],
        [ -2.5683, -10.4433,  -2.9182],
        [  0.4119,  14.1019,  -4.1870],
        [  6.3589,   0.8239,  -8.4230],
        [ -9.4630,  -1.5145,   0.2983],
        [  5.9548,  -1.2273,  -2.6520],
        [  5.7963,  -1.6018,   1.8856],
        [ -3.2736, -10.1703,   3.8712],
        [  4.1140,  -3.7220,  -0.1273],
        [  9.4925,   9.3811,   8.9842],
        [  6.0054,  -1.0902,   8.3079],
        [ -7.7239,   4.4298,   3.1216],
        [ -9.0604,   1.7707,   1.1066],
        [  1.6408,   7.4591,  -4.2294],
        [  6.3124,   0.2057,  -0.4593],
        [ 11.6801,  -3.7196,  -0.9181],
        [  2.3261,  13.7749,   5.9121],
        [  0.6142,  14.0802,   0.5407],
        [ -9.4716,  -0.6673,   7.6068],
        [ 11.5198,  -4.0923,   5.5088],
        [  2.0937,  13.8293,  -2.3533],
        [  6.9693,  -9.3200,  -8.3822],
        [  0.9788,  -4.8145,  -3.8661],
        [  6.3205,   1.7068,  -3.8619],
        [  5.9587,  12.3216,   9.1695],
        [ 12.4996,   2.6335,  -6.3166],
        [ -3.2736, -10.1703,   3.8712],
        [  3.2990,  -4.2415,  -7.4857],
        [  7.7750,  11.0665,   2.8364],
        [ -9.0604,   1.7707,   1.1066],
        [ -8.8154,   2.4611,   2.5198],
        [ 11.2847,  -4.5848,  -4.7503],
        [  1.1274,  14.0116,   8.1753],
        [  6.9433,  -9.3362,  -0.3421],
        [ -5.5525,   6.5146,  -4.4984],
        [  2.9410,   6.8428,   5.4458],
        [ -5.6792,  -8.7352,   4.0318],
        [  2.8994,   6.8675,  -9.5987],
        [  2.0547,   7.2957,  -1.9343],
        [  1.9312,  13.8649,   8.3563],
        [  8.4691,  10.4571,  -5.0650],
        [  7.5064,  -8.9651,  -0.0994],
        [  2.6451,  -4.5250,  -0.5565],
        [ -9.2301,  -3.1537,  -2.7477],
        [ 12.4690,  -0.8528,  -9.3374],
        [ 11.0864,   7.0387,  -0.1238],
        [  3.3943,   6.5483,   1.0790],
        [ -4.9217,   6.8979,  -1.7667],
        [ 12.4597,  -0.9136,  -4.8763],
        [  4.4633,   5.6287,  -0.7754],
        [  8.7131,  10.2216,   7.7915],
        [  5.6523,   3.9443,  -2.9449],
        [ -9.4296,  -1.9458,   4.0833],
        [ 10.3251,   8.2928,  -3.0006],
        [  1.4749,  -4.7892,  -0.8089],
        [  6.3301,   0.3638,  -7.5685],
        [  5.1203,  -2.7151,   6.2110],
        [  5.9526,   3.2525,  -4.3821],
        [  1.9204,   7.3518,   8.4781],
        [  4.5340,  -3.3629,   8.9652],
        [ -7.6650,   4.5092,   0.2520],
        [  5.7151,  -1.7700,   3.1542],
        [  3.6703,   6.3443,  -5.4401],
        [ -5.6792,  -8.7352,   4.0318],
        [ -1.1885, -10.8211,   0.0865],
        [  5.8889,  -1.3916,   8.8993],
        [  2.0449,  13.8402,  -7.1642],
        [ 10.4758,  -5.9539,   1.3667]]), 'num flow neighbors': 5, 'precomputed_distances': tensor([[0.0000, 0.6470, 0.6865,  ..., 0.1538, 1.0819, 0.5542],
        [0.6470, 0.0000, 0.0636,  ..., 0.4957, 1.0698, 0.4033],
        [0.6865, 0.0636, 0.0000,  ..., 0.5379, 1.0323, 0.3838],
        ...,
        [0.1539, 0.4957, 0.5379,  ..., 0.0000, 1.0674, 0.4639],
        [1.0819, 1.0698, 1.0323,  ..., 1.0674, 0.0000, 0.6888],
        [0.5542, 0.4033, 0.3838,  ..., 0.4639, 0.6888, 0.0000]]), 'neighbors': tensor([[0., 0., 0., 0., 0.],
        [1., 2., 3., 4., 5.]]), 'labels': array([14.10045797,  8.40445872,  8.44940661,  8.41148722,  8.37954853,
        8.24808832,  8.29203356,  9.3349858 ,  5.05981914,  8.51928531,
        6.32572323, 13.62896593, 12.62576026,  5.76165934, 11.75438006,
        7.822854  , 13.85158417,  7.83486943, 12.27991991,  7.76457095,
        9.84314712,  8.66273171, 10.14436912,  5.05963217, 13.05148826,
        7.01475376,  4.91038884,  7.69752262,  5.69913817,  7.39004226,
       13.50484539,  5.5513072 ,  8.41171369, 12.35421461,  5.51177501,
       12.10222204,  6.32572323, 11.42947632,  7.16058587, 10.75443106,
       14.10796466,  6.41202986,  9.58347456,  6.07992623,  6.01356004,
       10.68416401,  5.54776934, 13.34587027,  6.10360073,  8.90405823,
        9.23178204,  7.6374603 ,  6.31576264, 12.25806559, 13.96987806,
       14.09357547,  9.49511524, 12.22503754, 13.98691426, 11.63765273,
        4.91296205,  6.54693987, 13.68672855, 12.77402351, 10.68416401,
        5.37343173, 13.5247215 ,  9.23178204,  9.15253344, 12.18045978,
       14.05687815, 11.63502679,  8.55982105,  7.44805901, 10.41909211,
        7.4544866 ,  7.57946459, 13.99877413, 13.45642379, 11.69264243,
        5.24137909,  9.75401449, 12.4980845 , 13.13205357,  7.37576154,
        8.47371868, 12.49317563,  7.18354885, 13.43127131,  6.89245352,
        9.6282763 , 13.2430377 ,  5.01114719,  6.34059021,  5.79562691,
        6.78325151,  7.5984809 ,  5.64500512,  8.89301516,  5.98285319,
        7.32950385, 10.41909211, 10.88618114,  6.05113217, 13.99048094,
       12.0495521 ])}
{'P': tensor([[1.4647e-01, 1.0793e-01, 1.0610e-01,  ..., 1.2004e-03, 2.4085e-05,
         1.4957e-05],
        [4.7301e-05, 3.0546e-02, 3.8074e-02,  ..., 1.1099e-04, 1.9310e-05,
         4.7610e-05],
        [6.0276e-05, 2.0318e-02, 4.1110e-02,  ..., 1.5119e-04, 2.7962e-05,
         6.0019e-05],
        ...,
        [6.4641e-03, 2.9128e-02, 3.7600e-02,  ..., 8.2664e-02, 3.6953e-04,
         5.6547e-05],
        [1.3579e-03, 1.2664e-03, 1.4558e-03,  ..., 4.4682e-02, 6.2828e-02,
         8.6173e-05],
        [2.1449e-04, 5.5753e-04, 5.0492e-04,  ..., 8.3604e-04, 1.7294e-03,
         1.5102e-01]]), 'X': tensor([[ 4.1193e-01,  1.4102e+01, -4.1870e+00],
        [-3.9700e+00,  7.3453e+00, -4.1486e+00],
        [-4.0409e+00,  7.3169e+00, -3.5779e+00],
        [-4.1296e+00,  7.2803e+00, -2.7194e+00],
        [-5.2589e+00,  6.7024e+00, -5.5809e+00],
        [-5.5525e+00,  6.5146e+00, -4.4984e+00],
        [ 2.5010e+00, -4.5736e+00, -8.9890e-01],
        [ 6.3633e-01, -1.1035e+01,  6.1414e+00],
        [-3.3812e+00, -1.0123e+01,  7.4384e+00],
        [ 1.0757e+01,  7.6212e+00, -2.3279e+00],
        [-8.0608e+00,  3.9362e+00, -5.9567e+00],
        [-9.4309e+00, -5.9902e-02, -4.0830e+00],
        [ 6.2555e+00,  2.1474e+00,  4.1685e+00],
        [ 1.2469e+01, -8.5278e-01, -9.3374e+00],
        [-4.2271e+00,  7.2387e+00, -1.8316e+00],
        [-1.1885e+00, -1.0821e+01,  8.6494e-02],
        [ 1.0325e+01,  8.2928e+00, -3.0006e+00],
        [-3.1671e+00,  7.6158e+00,  6.0765e+00],
        [-9.2707e+00,  9.6612e-01,  4.4863e+00],
        [ 1.3670e+00, -4.7990e+00,  3.2603e+00],
        [ 7.1697e+00,  1.1534e+01, -7.2756e-01],
        [ 4.4633e+00,  5.6287e+00, -7.7540e-01],
        [ 5.8450e+00, -9.9356e+00,  3.0767e+00],
        [ 1.1902e+01, -3.1379e+00, -3.4534e+00],
        [-9.4157e+00,  8.2118e-02, -5.0025e+00],
        [ 6.3236e+00,  3.0105e-01, -4.6668e+00],
        [ 5.6414e+00, -1.0030e+01,  7.8525e+00],
        [ 1.1474e+01,  6.2478e+00, -2.1100e+00],
        [-8.9282e+00,  2.1648e+00,  8.4894e+00],
        [-5.0550e+00,  6.8231e+00, -9.2502e+00],
        [ 5.9526e+00,  3.2525e+00, -4.3821e+00],
        [-1.7009e+00,  7.8851e+00, -8.2437e+00],
        [ 6.1973e+00, -4.3723e-01,  6.5720e+00],
        [ 8.5198e+00,  1.0409e+01, -8.6486e+00],
        [ 1.1594e+01,  5.9740e+00, -4.3952e+00],
        [ 9.6614e+00,  9.1784e+00, -1.2087e+00],
        [ 4.7482e+00, -1.0391e+01,  5.9149e+00],
        [ 4.2096e+00,  5.8815e+00,  1.9230e+00],
        [ 1.1742e+01,  5.6070e+00, -1.4192e+00],
        [ 6.3301e+00,  3.6378e-01, -7.5685e+00],
        [-8.3717e+00, -5.4769e+00, -9.2228e+00],
        [ 2.0937e+00,  1.3829e+01, -2.3533e+00],
        [ 1.2520e+01, -4.7113e-01,  3.0436e+00],
        [ 1.1470e+01, -4.2006e+00,  7.4086e+00],
        [ 1.2004e+01, -2.8350e+00,  2.6864e+00],
        [ 9.3560e+00,  9.5391e+00,  9.4943e+00],
        [ 2.4572e+00,  7.1085e+00,  7.7376e+00],
        [ 9.1409e+00, -7.5789e+00,  1.5814e+00],
        [ 3.6817e+00,  6.3354e+00,  6.1233e+00],
        [ 6.1066e+00, -7.7986e-01, -4.1746e+00],
        [ 5.1667e+00, -2.6543e+00,  1.2879e+00],
        [-8.1426e+00,  3.8048e+00,  9.3542e+00],
        [ 5.6258e+00, -1.9404e+00, -6.0715e+00],
        [ 3.4604e+00, -4.1545e+00,  1.8091e+00],
        [ 3.4931e-01, -4.7727e+00, -6.5682e+00],
        [ 2.6613e+00,  7.0021e+00,  4.5783e+00],
        [ 1.1312e+01,  6.5957e+00, -4.5667e+00],
        [ 1.2572e+01,  1.9266e+00,  7.4903e+00],
        [ 4.2096e+00,  5.8815e+00,  1.9230e+00],
        [ 9.9756e+00, -6.6330e+00, -3.3429e+00],
        [ 1.7659e+00,  7.4127e+00,  4.7871e+00],
        [ 1.1780e+01, -3.4697e+00,  3.5624e+00],
        [-1.6257e-01, -1.0980e+01,  6.4629e+00],
        [ 7.1441e+00,  1.1553e+01,  2.3232e+00],
        [ 1.0506e+01, -5.9099e+00, -5.1599e+00],
        [-1.2454e+00,  7.9127e+00, -5.7153e-01],
        [-6.3231e-01,  7.9085e+00, -5.9544e+00],
        [ 3.4931e-01, -4.7727e+00, -6.5682e+00],
        [-8.5687e-01,  7.9156e+00, -6.5557e+00],
        [-8.8058e+00,  2.4850e+00, -1.7425e+00],
        [-7.2515e+00,  5.0195e+00,  4.6434e+00],
        [ 1.2565e+01,  2.0132e+00,  4.6272e+00],
        [-4.3415e-01, -1.0947e+01,  7.4509e+00],
        [ 5.2911e+00, -2.4824e+00, -3.6877e+00],
        [ 4.4049e+00,  5.6892e+00, -4.4394e+00],
        [ 6.3569e+00,  7.5912e-01,  6.5011e+00],
        [ 1.0391e+00, -4.8141e+00, -7.6827e-02],
        [-2.6485e+00, -1.0415e+01,  8.7660e-01],
        [-5.1369e+00,  6.7755e+00,  8.3836e+00],
        [ 4.7482e+00, -1.0391e+01,  5.9149e+00],
        [ 1.2292e+01, -1.7902e+00, -4.0870e+00],
        [ 2.5636e+00, -1.0929e+01,  9.6519e+00],
        [ 6.8407e+00,  1.1767e+01,  3.0045e+00],
        [-6.2668e+00,  5.9808e+00,  2.5614e+00],
        [ 1.6232e+00, -4.7717e+00, -2.5655e+00],
        [-3.7089e+00,  7.4434e+00, -1.7881e-03],
        [-8.8540e+00, -4.3971e+00, -5.2144e+00],
        [ 1.4973e-01,  7.8334e+00, -5.4412e+00],
        [ 4.9452e+00, -1.0319e+01, -7.8621e+00],
        [ 3.4009e+00, -4.1874e+00, -5.9751e+00],
        [ 7.1441e+00,  1.1553e+01,  2.3232e+00],
        [ 5.1203e+00, -2.7151e+00,  6.2110e+00],
        [-8.1905e+00,  3.7253e+00,  4.1175e+00],
        [ 1.2469e+01, -8.5278e-01, -9.3374e+00],
        [-7.6734e+00,  4.4980e+00, -5.4248e+00],
        [ 8.5198e+00,  1.0409e+01, -8.6486e+00],
        [ 7.6853e-01, -4.8098e+00, -2.9310e+00],
        [ 4.2096e+00,  5.8815e+00,  1.9230e+00],
        [ 6.3200e+00,  2.6900e-01,  1.5900e+00],
        [-8.4549e-01, -1.0885e+01, -6.7400e+00],
        [ 1.1895e+01, -3.1570e+00,  7.0742e+00],
        [ 6.3124e+00,  2.0571e-01, -4.5926e-01],
        [ 9.3607e+00,  9.5337e+00, -4.5412e+00],
        [ 1.8766e+00,  7.3694e+00,  1.1887e+00],
        [ 6.2022e+00,  2.4092e+00,  3.0349e+00],
        [ 4.0421e+00, -3.7765e+00, -8.3631e+00]]), 'num flow neighbors': 5, 'precomputed_distances': tensor([[0.0000, 0.4997, 0.5066,  ..., 0.4861, 0.5842, 0.1135],
        [0.4997, 0.0000, 0.0361,  ..., 0.4397, 0.6723, 0.4241],
        [0.5066, 0.0361, 0.0000,  ..., 0.4114, 0.6456, 0.4375],
        ...,
        [0.4861, 0.4397, 0.4114,  ..., 0.0000, 0.2362, 0.5108],
        [0.5842, 0.6723, 0.6456,  ..., 0.2362, 0.0000, 0.6475],
        [0.1135, 0.4241, 0.4375,  ..., 0.5108, 0.6475, 0.0000]]), 'neighbors': tensor([[0., 0., 0., 0., 0.],
        [1., 2., 3., 4., 5.]]), 'labels': array([14.10796466,  8.34949383,  8.35856487,  8.36995953,  8.51928531,
        8.55982105,  5.21280156, 11.05317597, 10.67322527, 13.18278606,
        8.97052115,  9.43112957,  6.61386436, 12.4980845 ,  8.38252937,
       10.88618114, 13.2430377 ,  8.24808832,  9.32094055,  4.98989906,
       13.58101794,  7.18354885, 11.52733581, 12.30858677,  9.41605684,
        6.33075682, 11.50791859, 13.06498554,  9.18690018,  8.49161154,
        6.78325151,  8.06643487,  6.21275016, 13.45124917, 13.04217487,
       13.32613445, 11.42420508,  7.23276582, 13.01187484,  6.34059021,
       10.00410625, 13.98691426, 12.52875793, 12.21532282, 12.3344536 ,
       13.3614598 ,  7.52117132, 11.87412439,  7.32754882,  6.1561646 ,
        5.80860165,  8.98765644,  5.9510489 ,  5.40689332,  4.78544875,
        7.49076899, 13.09426142, 12.71843462,  7.23276582, 11.97957425,
        7.62011734, 12.27991991, 10.98076873, 13.58333857, 12.05395056,
        8.01009083,  7.9337647 ,  4.78544875,  7.96181288,  9.14973319,
        8.81930525, 12.72524615, 10.95593729,  5.84450127,  7.19513806,
        6.4020404 ,  4.92497514, 10.74655346,  8.50268322, 11.42420508,
       12.4217523 , 11.22596994, 13.6105595 ,  8.66273171,  5.04028538,
        8.31625171,  9.88571713,  7.83486943, 11.4424816 ,  5.39450305,
       13.58333857,  5.79562691,  8.99791316, 12.4980845 ,  8.89458273,
       13.45124917,  4.87083348,  7.23276582,  6.32572323, 10.91805683,
       12.30695098,  6.31576264, 13.36092624,  7.60463349,  6.65368551,
        5.53175275])}
{% endraw %}

Dataloaders

Because we're handling batching in a, sahll we say, delicate way, the standard way of batching data doesn't work (without some downstream effort). In fact, we're treating each output element of the dataset as a batch by itself, so we can get nice behavior just by disabling batching entirely.

{% raw %} 
from torch.utils.data import DataLoader
dataloader = DataLoader(ds, batch_size=None)
{% endraw %} {% raw %} 
for d in dataloader:
    print(d["X"].type())

torch.FloatTensor
torch.FloatTensor
torch.FloatTensor
torch.FloatTensor
torch.FloatTensor
torch.FloatTensor
torch.FloatTensor
torch.FloatTensor
torch.FloatTensor
torch.FloatTensor
torch.FloatTensor
torch.FloatTensor
torch.FloatTensor
torch.FloatTensor
torch.FloatTensor
torch.FloatTensor
torch.FloatTensor
torch.FloatTensor
torch.FloatTensor
torch.FloatTensor
torch.FloatTensor
torch.FloatTensor
torch.FloatTensor
torch.FloatTensor
torch.FloatTensor
torch.FloatTensor
torch.FloatTensor
torch.FloatTensor
torch.FloatTensor
torch.FloatTensor
torch.FloatTensor
torch.FloatTensor
torch.FloatTensor
torch.FloatTensor
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{% endraw %}

Convenience functions

{% raw %}

dataloader_from_ndarray[source]

dataloader_from_ndarray(X, flow, labels)

{% endraw %} {% raw %}
{% endraw %} {% raw %} 
dataloader.dataset.X

tensor([[ 0.1206, -4.7363,  8.7103],
        [ 0.1532, -4.7422, -7.0145],
        [ 0.1677, -4.7447, -6.1529],
        ...,
        [ 0.6142, 14.0802,  0.5407],
        [ 0.5175, 14.0910,  4.6540],
        [ 0.4119, 14.1019, -4.1870]])
{% endraw %}